### Transformation of Graphs - translation

f(x) → f(x + a) - a translation in the negative x-axis by a f(x) → f(x - a) - a translation in the positive x-axis by a f(x) → f(x) + a - a translation in the positive y-axis by a f(x) → f(x) - a - a translation in the negative y-axis by a E.g.1 Sketch y = x 2 + 2x - 3 and find the following: The line of symmetry The solutions when y = 0 The coordinates of the minimum point The y-intercept y = x 2 + 2x - 3 By completing the square, y = (x + 1) 2 - 4 1) Line of symmetry, x = -1 2) (x + 1) 2 - 4 = 0 → x = -3 or x = 1 3) Turning point ~ (-1,-4) 4) y-intercept ~ (0,-3) E.g.2 Sketch y = x 2 -4x + 3 and find the following: The line of symmetry The solutions when y = 0 The coordinates of the minimum point The y-intercept y = x 2 -4x + 3 By completing the square, y = (x - 2) 2 - 1 1) Line of symmetry, x = 1 2) (x - 2) 2 - 1 = 0 → x = 3 or x = 1 3) Turning point ~ (2,-1) 4) y-intercept ~ (0,3) You can practise translation interactively with the following applet: